On page 62, Harry asks Dumbledore what Inferi are: “They are corpses,” said Dumbledore calmly. “Dead bodies that have been bewitched to do a Dark wizard’s bidding.”

Later in the book, we see an army of Inferi which Voldemort has set to guard one of his treasures:

The surface of the lake was no longer mirror-smooth; it was churning, and everywhere Harry looked, white heads and hands were emerging from the dark water, men and women and children with sunken, sightless eyes were moving toward the rock: an army of the dead rising from the black water. (Pg. 575)

In Latin, the word Inferi means “those down below, the dead”. The Dictionary of Greek and Roman Biography and Mythology says:

INFERI, signifies the gods of the lower world, in contradistinction from those of heaven, or from the Olympian gods... But the word inferi is still more frequently used to designate the dead, in contradistinction from those living upon the earth; so that apud inferos is equivalent to "in Hades," or "in the lower world." The Inferi therefore comprise all the inhabitants of the lower world, the gods, viz. Aides or Pluto, his wife Persephone, the Erinnyes, and others, as well as the souls of departed men. (Smith)

I find no reference in Greek or Roman mythology to anyone re-animating the bodies of the dead to make them walk about and do things for the magician who re-animates them. This idea of re-animating the dead seems to come from the idea of zombies, which idea arises from the voodoo traditions of the Caribbean.

However, Rowling, in her books, makes frequent use of Latin for her creatures, curses, and incantations, so in Harry Potter and the Half-Blood Prince, she seems to have combined the idea of zombies with the Latin word for the dead to create her Inferis.